2.9. THE PROBABILISTIC FATIGUE DAMAGE THEORY (THE K-D MODEL) 101
to create a MATLAB program. e iterative results are listed in Table 2.59. From the iterative
results, the reliability index ˇ and corresponding reliability R of the shaft in this example are:
ˇ D 1:705804 R D ˆ
.
1:705804
/
D 0:9560:
Table 2.58: e distribution parameters of random variables in Equation (e)
K (lognormal) M (klb.in) d (in)
μ
lnK
σ
lnK
μ
M
σ
M
μ
d
σ
d
41.738 0.357 21.34 1.31 2.150 0.00125
Table 2.59: e iterative results of Example 2.31 by the R-F method
Iterative #
K
*
M
*
d
*
β
*
|∆β
*
|
1 1.43E+18 21.34 2.081 1.722323
2 8.29E+17 23.18013 2.15866 1.706654 0.015669
3 9.18E+17 23.11098 2.150319 1.705806 0.000849
4 9.24E+17 23.11206 2.149932 1.705804 1.81E-06
2.9.11 RELIABILITY OF A COMPONENT WITH THE K-D MODEL BY
THE MONTE CARLO METHOD
e Monte Carlo method is displayed in Appendix A.3. In order to use the Monte Carlo method
to calculate the reliability of a component, we must establish its limit state function. When the
K-D model is used to describe the component fatigue strength index K and the component
fatigue damage index D, we can establish limit state functions for every possible cyclic loading
case.
When component is under simple cyclic loading, that is, cyclic axial loading, cyclic shear-
ing loading, cyclic torque loading, or cyclic bending loading, we can use Equation (2.87) to
establish a limit state function when simple cyclic loading can be described by model #1, #2,
and #3 cyclic loading spectrums. We can use Equation (2.88) to establish a limit state function
when simple cyclic loading can be described by model #4, #5, and #6 cyclic loading spectrums.
For cyclic combined loading on a rotating shaft, we can use Equation (2.95) to establish
a limit state function.
When a limit state function is established, we can use the Monte Carlo method to cal-
culate the reliability of a component under a cyclic loading spectrum. Lots of examples in Sec-
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